$2\left( 1-{{\cos }^{2}}x \right)+9\operatorname{cosx}+3=0\Rightarrow 2-2{{\cos }^{2}}x+9\operatorname{cosx}+3=0\Rightarrow 2{{\cos }^{2}}x-9\cos -5=0$  $\Rightarrow \left( 2\operatorname{cosx}+1 \right)\left( \operatorname{cosx}-5 \right)=0\Rightarrow \left\{ \begin{matrix}    \operatorname{cosx}=5  \\    \operatorname{cosx}=-\frac{1}{2}  \\ \end{matrix} \right.$  $\operatorname{cosx}=-\frac{1}{2}=\cos \frac{2\pi }{3}\Rightarrow x=2k\pi \pm \frac{2\pi }{3}$